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For $M\in R$-Mod, $N\subseteq M$ and $L\in \sigma \left[ M \right] $ we consider the product $N_{M}L=\sum_{f\in {\rm Hom}_{R} ( M,L ) }f ( N ) $. A module $N\in \sigma \left[ M\right] $ is called an $M$-multiplication module if for every submodule $L$ of $N$, there exists a submodule $I$ of $M$ such that $L=I_{M}N$. We extend some important results given for multiplication modules to $M$-multiplication modules. As applications we obtain some new results when $M$ is a semiprime Goldie module. In particular we prove that $M$ is a semiprime Goldie module with an essential socle and $N$ $\in \sigma \left[ M\right] $ is an $M$ -multiplication module, then $N$ is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.
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참고문헌 (19)
참고문헌 신청
D. D. Anderson / 1980 / Some remarks on multiplication ideals / Math. Japon 25(4):463~469
D. D. Anderson / 2000 / Some remarks on multiplication ideals. II / Comm. Algebra 28(5):2577~2583
A. Barnard / 1981 / Multiplication modules / J. Algebra 71(1):174~178
J. A. Beachy / 2002 / M-injective modules and prime M-ideals / Comm. Algebra 30(10):4649~4676
L. Bican / 1980 / Prime and coprime modules / Fund. Math 107(1):33~45
D. D. Anderson / 2000 / Some remarks on multiplication ideals. II / Comm. Algebra 28(5):2577~2583
A. Barnard / 1981 / Multiplication modules / J. Algebra 71(1):174~178
J. A. Beachy / 2002 / M-injective modules and prime M-ideals / Comm. Algebra 30(10):4649~4676
L. Bican / 1980 / Prime and coprime modules / Fund. Math 107(1):33~45
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